Question 359: Waves

Question

A progressive wave is given by, $$\mathrm{Y}=12 \sin (5 \mathrm{t}-4 \mathrm{x})$$. On this wave, how far away are the two points having a phase difference of $$90^{\circ}$$ ?

Accepted Answer

$$\begin{aligned}
& 	ext { Given, } y=12 \sin (5 t-4 x) \
& 	herefore \quad y=12 \sin 2 \pi\left(\frac{5 t}{2 \pi}-\frac{4 x}{2 \pi}ight)
\end{aligned}$$
Comparing above eq. with, $$y=A \sin 2 \pi\left(\frac{x}{\lambda}-\frac{t}{T}ight)$$
We get, $$\lambda=\frac{2 \pi}{4}$$
Relation between phase difference and path difference is
$$\begin{aligned}
\Delta \phi & =\frac{2 \pi}{\lambda} \Delta \mathrm{x} \
	herefore \quad \frac{\pi}{2} & =\frac{2 \pi}{\left(\frac{2 \pi}{4}ight)} \Delta \mathrm{x} \
	herefore \quad \Delta \mathrm{x} & =\frac{\pi}{8}
\end{aligned}$$

Answer

$$\frac{\pi}{4}$$

Answer

$$\frac{\pi}{8}$$

Answer

$$\frac{\pi}{16}$$

Answer

$$\frac{\pi}{32}$$

Waves

A progressive wave is given by, $\mathrm{Y}=12 \sin (5 \mathrm{t}-4 \mathrm{x}). On this wave, how far away are the two points having a phase difference of 90^{\circ}$ ?

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